Exam 1 Suggested Exercises
Math 150
Directions: In this document you will find seventeen questions I have written for your practice. I would recommend you work through all of these to make sure you’re familiar with not only the concepts presented in each section but also the types of questions that are associated with these topic. Solutions to these exercises are in a separate document on your course website. If you have any questions send me an email, ask during class, or see me during office hours.
Question 1) Decide if the following variables are categorical or quantitative. (a) Social Security Numbers
(b) Square footage of a house (c) Number of pets owned (d) Native Language
Question 2) Suppose that a large company wants to know more about its employees’ views on the company. To do this they break down their company into four major departments, Financial Services, Network Services, Customer Services, and Support Staff. Then they randomly choose 10 people from each department to answer a survey. Out of the 40 people who are randomly selected 34 respond to the survey. The survey asks each person the number of years they have been working at the company, if they would consider themselves Very Satisfied, Satisfied, or Not Satisfied with their job, and finally would they recommend working at this company to a friend (Yes/No). (a) What is the population of interest?
(b) What is the sample?
(c) What type of sampling technique was used to build this sample? (d) What were the individuals in this sample?
(e) How many variables were collected about each individual? Classifiy each of these variables as Categorical or Quanitative.
Question 3) Suppose you take a sample of 200 people and ask them the color of their car. You get the following data:
White: 50 Black: 40 Silver: 40 Gray: 20 Red: 15 Blue: 10 Tan: 10 Other: 15
(a) Construct a relative frequency table for this data.
(b) Using the data from this question construct a pie chart displaying this data.
(c) Using the data from this question construct a relative frequency bar graph displaying this data. (d) How many cars were White or Black?
(e) What percentage of the cars in the sample were not Blue?
Question 4) Here are the batting averages for 20 randomly selected baseball players. (Note: Batting averages are measured as decimals calculated by dividing the number of hits a player has by their number of attempts).
.223, .226, .230, .233, .233, .235, .237, .238, .241, .245
.245, .246, .249, .250, .255, .258, .261, .266, .288, .309
(a) Construct a histogram for this data starting at .220 with a class size of .010. What is the
shape of this distribution?
(b) Using the data from this question calculate the mean, median, and standard deviation of the data. Does the relationship between mean and median agree with the shape you found in part (a)?
Question 5) Suppose you are studying three NBA players. You observe ten games for each player and record their points scored each game. You get the following data:
Player 1: 16,22,5,15,32,23,25,15,19,25
Player 2: 11,13,14,20,15,16,18,12,9,11
Question 6) Describe the most likely shape for each of the following variables. (a) Number of times a US adult eats fast food in a month
(b) Weight in pounds of a male El Camino student (c) Scores on an easy exam
(d) Value rolled on a fair six-sided die
Question 7)
(a) Give the 5 number summary for this data in Problem 4. Then construct a box plot of this data. (b) Are there any outliers in this data? Why or why not?
Question 8) Suppose that the weights of adult black bears are approximately normally distributed with a mean of 320 pounds and a standard deivation of 80 pounds.
(a) What is the chance that an adult black bear weighs more than 300 pounds? (b) What is the chance that an adult black bear weighs less than 500 pounds? (c) What is the chance that an adult black bear weighs more than 650 pounds?
(d) If an adult black bear was at the 85th percentile in terms of weight, how much did it actually weigh in pounds?
Question 9) Suppose that reaction times for both adults (age 30) and adults (age 50) are approx-imately normally distributed. Adults, age 30, have an average reaction time of 225 milliseconds with a standard deviation of 40 milliseconds. Adults, age 50, have an average reaction time of 250 milliseconds with a standard deviation of 30 milliseconds.
(a) What is the chance that a randomly selected adult (age 30) will have a reaction time less than 200 milliseconds?
(b) What is the chance that a randomly selected adult (age 50) will have a reaction time greater than 300 milliseconds?
(c) Suppose that Arthur (age 30) has a reaction time of 190 millseconds while Bob (age 50) has a reaction time of 215 milliseconds. Who, relative to their age, has a better reaction time?
Question 10) Suppose that you are taking two classes, a very difficult math class and a pretty easy art history class. Recently, you’ve taken an exam in both classes. You learn that on the math test that the scores were approximately normally distributed with an average of 60 points and a standard deviation of 13 points. The scores on the art history test were also approximately normal but with an average of 87 points and a standard deviation of 4 points.
(a) What percent of students scored above a 70 on the math test?
(b) What percent of students scored between an 80 and a 90 on the art history test?
(c) Your friend tells you they scored in the 92nd percentile on the math test. What was their actual point score on the math test?
(d) If you scored a 74 on the math test and a 92 on the art history test on which test did you do better on relative to the other students?
Question 11) Suppose I’m interested in the average commute time for El Camino students. I survey 20 randomly selected students and ask them, ”How long does it usually take you to get to school in the morning?” I get the following results (all values are in minutes).
3,6,8,11,13,14,14,15,18,20,20,20,22,23,25,25,28,30,35,40
(a) Calculate the mean and standard deviation of this data set.
(b) Create a histogram to represent this data using a class width of 6 starting at 0. Describe the shape of the distribution.
(c) Would it be appropriate to apply the Empirical Rule here? Why or why not?
(d) Regardless of your answer to (c) between what two values should 68% of the data land? (e) What percent of the data actually lands between the two values you listed in (d)?
Question 12) Suppose that HBO is interested in estimating how many hours a day the average Amer-ican spends watching television. To do this they randomly select 1000 people who are currently on the HBO mailing list (either from having signed up online or having paid for HBO at some point) and email them a short survey. One of the questions asks ”How many hours do you spend watching TV each day?”. They get responses from 145 people and summarize the data in the following table.
Hours of TV Watched Frequency
0 to 2 55
2 to 4 51
4 to 6 24
6 to 8 12
8 to 10 3
(a) Construct a histogram from this frequency table. Describe the shape of the distribution. (b) Approximate the mean and standard deviation for the number of hours of TV watched in this survey.
(c) What percent of people surveyed reported that they watched 6 or more hours of TV a day? (d) Describe two forms of bias in this study.
Question 13) I am interested in studying the prevalence of shoplifting around the Torrance area. I decide to walk around the El Camino College campus and ask people that I see, ”How many times have you stolen something in the past year?”. I ask around 300 people and gather 30 actual responses.
(a) What type of sampling is this?
(b) Name at least four sources of bias in this study and make sure to describe where each one comes from.
Question 14) Suppose I am interested in studying how alcohol affects people’s perception of attrac-tiveness. To do this I gather 300 random subjects. I randomly choose one third of these subjects, give them each one alcoholic drink, and then show them a series of 10 headshots and ask them to rate the attractivenss of each person (on a scale of 1 to 10). Next, I take another random third of my subjects, give them each two alcoholic drinks, and then show them the same series of 10 headshots and ask them to rate the attractivenss of each person. Finally, I bring in the last third of the subjects. This group each receives three alcoholic drinks. I show them the 10 headshots and ask them to rate the attractivenss of each person. After this I average all the attractiveness ratings from each group and compare the results.
(a) What is the goal of this experiment?
(b) What is the response variable? What is the explanatory variable? (c) What type of experiment is this?
(d) How many treatments are there? What are they?
(e) Is there a control group in this experiment? If so, which group is it? If not, how coud you add one to the experiment?
(f) Would it be possible to introduce a placebo treatment into this experiment? How would you do it?
Question 15) Suppose I want to conduct an experiment about that studies the effects of pres-sure on academic performance. I randomly gather 100 high school aged students. On Day 1 of the experiment I bring them all into a large classroom and give them a 20 minute test on basic arithmetic and algebra. After the exam I record their scores. The next day I once again bring them to the large classroom and announce that they are going to take another arithmetic/algebra test but this time each student’s score will be announced in front of everyone else. Again they take the same test and I compare the scores from Day 1 and Day 2.
(a) What is the goal of this experiment?
(b) What is the explanatory variable? What is the response variable? (c) What type of experiment is this?
(d) How many treatments are there in this experiment? What are the treatments?
Question 16) Suppose you are interested in studying the relationship between academic perfor-mance and salary as a working adult. You randomly select 400 adults who are currently working and record their current salary. Then you find all their school records and analyze their past aca-demic performance. After doing this you find statistically significant evidence that students who did better ended up having higher salaries.
(a) Is this an observational study or an experiment? (b) What type of study or experiment is this?
(c) What is the explanatory variable? What is the response variable?
(d) Would it be correct to conclude from this study that doing better in school causes you to have a higher salary in the long run?
Question 17) Suppose that I am interested in studying the affect of motivation on academic per-formance. I randomly select 500 students. I first divide these students by gender. Then in each gender group I randomly divide them into thirds. One third of the students have a person come in and give them a motivational speech about the importance of academics. One third of the students have a person come in and give them a speech about how education is ultimately unimportant. The final third of the students have a person come in and talk to them about an unrelated topic. After this the students all do several academic tasks such as doing worksheets or working through group problems and their performance is assessed.
(a) What type of experiment is this?
(b) What is the explanatory variable? What is the response variable?
(c) How many treatments are there? Is there a control group? Is there a placebo treatment? Explain.
SUGGESTED TEXTBOOK EXERCISES from Moore ”The Basic Practice of Statistics” Chapter 1: 1.13-1.22, 1.23-1.27, 1.29-1.33, 1.38, 1.40, 1.42
Chapter 2: 2.15-2.24, 2.25-2.26, 2.28, 2.31, 2.44, 2.50 Chapter 3: 3.15-3.24, 3.26-3.42, 3.46, 3.47, 3.49
Chapter 8: 8.17, 8.18, 8.20, 8.21, 8.24, 8.25, 8.26-8.28, 8.30-8.34 Chapter 9: 9.19-9.28, 9.29-9.34, 9.38, 9.46, 9.50
